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The  Weight  of  a  Falling  Drop  and  the 

Laws  of  Tate.    The  Drop  Weights 

and  Molecular  Weights  of  Some 

of  the  Lower  Esters 


DISSERTATION 

SUBMITTED  IN  PARTIAL  FULFILMENT  OF  THE  REQUIRE- 
MENTS FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 
IN  THE  FACULTY  OF  PURE  SCIENCE  IN  COLUMBIA 
UNIVERSITY  IN  THE  CITY  OF  NEW  YORK. 


BY 

FREDERICK  W.  SCHWARTZ 

NEW  YORK  CITY 
1911 


EASTON,  PA.: 

ESCHBNBACH  PRINTING  Co, 
1911. 


The  Weight  of  a  Falling  Drop  and  the 

Laws  of  Tate,    The  Drop  Weights 

and  Molecular  Weights  of  Some 

of  the  Lower  Esters 


DISSERTATION 


SUBMITTED  IN  PARTIAL  FULFILMENT  OF  THE  REQUIRE- 
MENTS FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 
IN  THE  FACULTY  OF  PURE  SCIENCE  IN  COLUMBIA 
UNIVERSITY  IN  THE  CITY  OF  NEW  YORK. 


BY 

FREDERICK  W.  SCHWARTZ 

NEW  YORK  CITY 

1911 


EASTON,  PA.: 

ESCHENBACH  PRINTING  Co. 
1911. 


ACKNOWLEDGMENT. 

To  Professor  J.  Livingston  R.  Morgan  the  author  wishes  to 
express  his  sincere  thanks  for  advice,  assistance  and  encourage- 
ment afforded  him  throughout  the  work.  F.  W.  S. 


226927 


CONTENTS. 

Introduction  and  object  of  the  investigation 5 

Apparatus  and  method 6 

Results. ...!... 8 

Summary 23 


The  Weight  of  a  Falling  Drop  and  the  Laws 

of  Tate.1    The  Drop  Weights  and 

Molecular  Weights  of  Some 

of  the  Lower  Esters* 


OBJECT  OF  THE  INVESTIGATION. 

As  has  been  shown  in  former  researches,2  the  weight  of  a 
drop  of  liquid  falling  from  a  properly  constructed  tip  is  pro- 
portional, for  any  one  diameter  of  tip,  to  the  surface  tension 
of  the  liquid;  and  further,  that  when  falling  drop  weights  are 
substituted  for  surface  tensions  in  the  formula  of  Eotvos,3 
as  modified  and  presented  by  Ramsay  and  Shields,4  the  molec- 
ular weights  and  critical  temperatures  of  liquids  can  be  calcula- 
ted with  an  accuracy  equal  to  that  attained  by  the  use  of  the 
surface  tensions  from  the  capillary  rise  method,  notwith- 
standing the  statements  of  Guye  and  Perrot5  to  the  contrary. 
The  object  of  this  investigation  has  been  the  testing  of  the 
new  definition  of  normal  molecular  weight  in  the  liquid  state 
as  given  by  Morgan  and  the  comparison  of  the  surface  tensions 
and  critical  temperatures  of  some  of  the  lower  esters,  deter- 
mined by  capillary  rise  and  drop  weight  methods.  The  esters 
chosen  for  this  investigation  were  methyl  formate,  ethyl 
formate,  propyl  formate,  amyl  formate,  methyl  acetate,  ethyl 
acetate,  propyl  acetate,  methyl  propionate,  ethyl  propionate, 
methyl  butyrate  and  methyl  isobutyrate. 

With  the  aid  of  a  simple  form  of  apparatus  devised  by 
Professor  Morgan,  the  determination  of  the  drop  weights  of 

1  Tate,  Phil.  Mag.,  4th  Ser.,  27,  176  (1864). 

2  Morgan  and  Stevenson,  Jour.  Am.  Chem.  Soc.,  30,  No.  3;    Morgan 
and  Higgins,  Jour.  Am.  Chem.  Soc.,  30,  No.  7. 

3  Eotvos,   Wied.  Ann.,  27. 

4  Ramsay  and  Shields,  Zeit.  phys.  Chem.,  12,  1893. 

5  Guye  and  Perrot,  Arch.  Sci.  Phys.  et  Nat.,  4  s.,  n  (1901);  4  s.,  15 
(1903). 


liquids  has  been  rendered  more  simple  than  by  the  methods 
used  by  Morgan  and  Higgins  and  Morgan  and  Stevenson. 

APPARATUS  AND  METHOD. 

The  apparatus  and  methods  used  were  the  same  as  de- 
scribed by  Morgan.1  The  chemicals  with  the  exception  of  amyl 
formate  were  manufactured  especially  for  this  investigation 
by  the  Hoffman  and  Kropff  Chemical  Company,  and  were 
exceptionally  pure  and  gave  entire  satisfaction.  The  amyl 
formate  was  obtained  from  Messrs.  Kimer  and  Amend  and  was 
purified  before  use. 

The  following  symbols  and  abbreviations  have  been  use 
throughout  this  work  : 

/  =  centigrade  temperature. 
Tc  =  critical  temperature. 

A  =  weight  in  grams  of  vessel  plus  25  drops  of  liquid. 
B  =  weight  in  grams  of  vessel  plus  5  drops  of  liquid. 
C  =  average  weight  in  grams  of  vessel  plus  25  drops  of 

liquid. 
D  =  average  weight  in  grams  of  vessel  plus  5  drops  of 

liquid. 

D.  W.  =  weight  in  milligrams  of  one  drop  of  liquid. 
K  =  drop  weight  constant. 
K'  =  surface  tension  constant. 
f  =  surface  tension  hi  dynes  per  square  centimeter. 
d  =  density. 

M  =  molecular  weight  in  the  liquid  state. 
For  the  calculation  of  K  the  following  modified  equation  of 
Ramsay  and  Shields  has  been  used. 


—  -  where  W  =  the  drop  weight  in  milligrams. 

Tc  —  (t  +  6) 

Surface  tension  being  proportional  to  drop  weights,  as 
shown  by  Morgan  the  following  equation  was  used  to  calculate 
surface  tension  : 

f  =  -  —  ^  —  —  ,  from  the  proportion,  ?  :  D.  W.  ::  K'  :  K. 
JK. 

1  Morgan,  Jour.  Am.  Chem.  Soc.,  33,  No.  3.  ; 


STANDARDIZATION  OF  TIP. 


Benzene. 

,  M  = 

78.  Tc  = 

288.4°. 

t' 

A. 

B. 

c. 

D. 

D.W. 

10.  0 

7 

•6515 

7.0063 

7 

.6516 

7.0062 

7 

•6515 

7  .  0064 

7 

.6514 

7.0063 

7  6515 

7.0063 

32.26 

40.7 

ii 

•0195 

10.4610 

ii 

.0194 

10.4612 

ii 

.0194 

10.4611 

ii 

•0193 

10.4611 

ii  .0194 

I0.46II 

27-9I5 

t. 

d. 

D.  W. 

w(M)2/s- 

K. 

Mean  K. 

10.  0 

o 

•8895549 

32.26 

636  .  72 

2-3374 

40.7 

0 

.8568299 

27.915 

564  .  90 

2-3372 

2-3373 

Pyridine. 

M  =  79-  T,  = 

346.6°. 

/. 

A. 

B. 

c. 

D. 

D.W. 

0.  I 

8 

•5643 

7.6986 

8 

•5642 

7.6984 

8 

•5643 

7-6984 

8 

•5644 

7.6985 

8.5643 

7-69847 

43  292 

34.25 

ii 

7086 

10.9472 

ii 

7084 

10-9472 

ii 

7085 

10.9474 

ii  . 

7087 

!0-9475 

ii  . 

7088 

10.9472 

I  I  .  7086 

10.9473 

38.005 

t. 

d. 

D.W. 

W(M)2/3- 

K. 

Mean  K. 

0.  I 

i  . 

0014     43.292 

796.31 

2-3359 

34-25 

0. 

9672     38.005 

716.58 

2  •  336o 

2-33595 

The  diameter  of  the  tip  was  5.53  millimeters. 

The  constant  used  throughout  the  work  was  the  benzene 
constant  2.3373.  In  the  standardization  of  the  tip,  only  the 
results  given  by  benzene  were  used,  in  order  to  make  com- 
parisons with  the  results  of  other  observers  who  also  used 
benzene  as  a  standardizing  liquid.  The  K  used  was  found 
by  use  of  the  modified  Ramsay  and  Shields  formula  using  the 
various  benzene  values. 

The  surface  tensions  were  all  calculated  from  the  formula 
as  given  previously,  K'  being  the  constant  given  by  the  in- 
vestigators who  used  the  capillary  rise  method. 


8 

DISCUSSION  OF  RESULTS. 
NEW  LIQUIDS. 

In  Tables  24-48  are  given  the  wf—  j     and  the  Tc  values 

/M\8/3 
calculated  from  K  in  the  relationship  W  (  -=  J     =  K  (Tc  —  t  —  6) 

using  the  molecular  weights  of  Young  and  Thomas, 
together  with  the  values  from  capillary  rise.  It  will  be  re- 
membered here  that  normal  molecular  weight  (Morgan)  is 
shown  by  the  attainment  of  the  same  calculated  value  of  Tc  from 

/M\s>» 
the  equation  W(  -j  J     =  K(TC  —  t  —  6)  at  all  temperatures  of 

observation. 

Agreement  of  the  values  of  Tc  from  drop  weight  and  surface 
tension  would  show  then  further,  that  D.  W.  :  7-  ::  K  :  K', 
for  the  molecular  weight,  is  the  same  and  the  density  is  the 
same  function  of  temperature  in  all  cases.  To  prove  the 
relationship  D.  W.  :  7-  ::  K  :  K/  directly,  the  values  of  7-  are 
given  both  from  drop  weight  and  from  curves  in  Tables  12-23. 

In  Tables  i-n,  the  experimental  results  are  given  for  the 
esters.  The  agreement  between  the  results  of  any  one  liquid 
at  any  one  temperature,  show  that  great  accuracy  may  be 
attained  in  every  case.  An  examination  of  columns,  A,  B, 
C,  D,  in  these  tables  shows  in  some  series  great  differences  at 
various  temperatures  due  to  various  weighing  vessels  used. 

In  Tables  12-23  are  comparisons  of  the  surface  tensions  by 
drop  weight  and  capillary  rise  methods.  It  will  be  seen  that 
remarkable  agreements  are  obtained  in  nearly  all  cases,  even 
in  those  in  which  the  results  were  extrapolated  far  beyond  the 
experimental  points.  It  is  to  be  doubted  in  some  cases  where 
the  agreement  is  not  very  close,  that  the  K'  for  benzene  from 
capillary  rise  was  determined  with  as  great  accuracy  as  it  was 
for  the  esters.  This  is  to  be  especially  noted  in  Table  14. 

In  Tables  16-23  the  disagreement  of  the  results  of  Ramsay 
and  Aston  with  tubes  of  different  radii  is  often  greater  than 
when  compared  with  those  results  taken  from  the  curve. 


9 
TABLE  i. — Methyl  formate. 

/.         A.          B.  C.          D.        D.  W. 

o.i    8.2323   7.6345 

8.2323  7-6345 
8.2325  7-6345 

8.2324  7-6346  8.23237  7-63452  29.893 
6.7   8.3898  7.8125 

8.3898  7.8126 

8.3897  7-8125 
8.3897  7.8126  8.38975  7-81255  28.86 

10.  o          7-5554  6.9906 

7-5553  6.9906 

7-5554  6.9904 

7-5555  6.9906       7-5554         6.99055     28.243 

16.4         8.3485  7-8013 

8.3486  7-8013 

8.3485  7-8013 

8.3484       7-8013       8.3485         7-8013       27.36 

27.82  8.3071  7-7948 
8  -  3072  7 • 7949 
8.3071  7-7949 

8.3073       7-7950       8.30717       7  7949       25.614 
TABLE  2. — Ethyl  formate. 

o.i         8.1827  7.6228 

8.1827  7.6230 

8.1828  7.6230 
8.1828  7.6231 

7.6231   8.18275   7.6229   27.993 

6.0    8.3243  7-7809 

8.3243  7.7810 
8 . 3242  7 . 7808 

8.3244  7-7809   8.3243    7-7809   27.17 
10. o    8.3355  7.8028 

8.3358  -7-8030 

8-3357  7-8029 

8-3357   7-8030   8.33567   7.80292  26.638 

17.0    8.2888  7-7751 

8.2886  7-7752 

8.2889  7-7753 

8.2889  7-7752   8.2888    7-7752   25.68 

33  95   10.9059  10.4381 

10.9058  10.4382 

10.9059  10.4380 

10.9060  10.4383  10.9059   10.43815  23.388 


10 


TABLE  3.  —  Propyl  formate. 

A. 

B. 

C.                          D.                   D.  W. 

7.5616 

6  -  9895 

7-56I5 

6.9895 

7-56I5 

6  .  9894 

7-56I5 

6.9894 

7  .  561  52       6  .  98945!  28  .  604 

8.3638 

7  •  8050 

8.3639 

7  8050 

8.3638 

7  •  8050 

8-3638 

7  .  8050 

8.36382       7-8050       27.941 

8  .  3492 

7  .  8026 

8-3494 

7.8027 

8  •  3494 

7.8027 

8  •  3494 

7.8025 

8.34935S:7  -80262     27.337 

8-3283 

7  7992 

8.3284 

7.7992 

8.3284 

7  •  7992 

8.3283 

7  •  7992 

8-32835       7-7992       26.458 

7-4595 

6-9733 

7-4593 

6-9735 

7-4594 

6.9736 

7-4595 

6-9735 

7.45942       6.97347     24.298 

7  •  3903 

6.9620 

7  •  3903 

6.9619 

7  •  3902 

6.9619 

7  •  3905 

6.9619 

7  •  3902 

7.3903         6.96192     21.419 

5-4 


10. o 


17.0 


34-75 


60.3 


TABLE  4. — Amyl  formate. 

10. o    8.3484  7-7993 

8 . 3486  7 . 7992 

8.3485  7-7992 

8.3485  7-7992   8.3485    7-79922  27.464 

35.0    8.2813  7-7875 

8.2813  7-7875 

8.2814  7-7875 

8.2812  7-7875   8.2813    7-7875   24.69 

60.  i    8.2176  7  7796 

8.2176  7-7796 

8.2177  7-7797 
8.2177  7-7795 

8.2177  8.21767   7.7796   21.904 


II 
TABLE  5. — Methyl  acetate. 

A.  B.  ~C.  D.  D.  W. 

o.i          8.2152       7.6292 

8.2151  7.6291 
8.2I5O    7.6291 

8.2152  7.6290    8.2I5I2     7.6291     29.301 

10. O 


34-20 


0.  I 


34.60 


60.5 


0.  I 


34.60 


60.  I 


6  .  8070 

6.2510 

6  .  8069 

6.2509 

6  .  8068 

6.2508 

6  .  8068 

6.2507 

6.80687   6.25085 

27.801 

8.2822 

7  7990 

8.2823 

7.7991 

8.2822 

7.7991 

8.2824 

7.7991 

8.28227   7.79907 

24.  16 

TABLE  6.  —  Ethyl  acetate. 

7-5421 

6.9834 

7-5420 

6.9834 

7-5421 

6.9832 

7-5422 

6.9832 

7.5421    6.9833 

27.94 

7.4442 

6.9767 

7-4443 

6.9768 

7-4443 

6.9767 

7.4442 

6.9769 

7.4442 

6  .  9766 

7.44424   6.97674 

23-375 

7-3658 

6  .  9646 

7.3659 

6  .  9647 

7-3659 

6  .  9646 

7  3660 

6  .  9646 

7-3659    6.96462 

20.064 

TABLE  7.— 

-Propyl  acetate. 

8.  1884 

7.6199 

8.1885 

7.6198 

8.1886 

7.6199 

8.1887 

7.6200 

8.18855   7-6199 

28-433 

7.4602 

6.9773 

7-4603 

6.9773 

7.4602 

6.9772 

7  .  4602 

6.9773 

7.46022   6.97727 

24.  148 

ii  .  1213 

10.6972 

ii  .  1216 

10.6973 

11.1215 

10.6974 

11.1215 

10.6974 

11.12147  10.69732 

2  I  .  208 

12 

TABLE  8. — Methyl  propionate. 

A.         B.  C.          D.        D.  W. 

6.8100  6.2513 

6. 8102  6.2513 

6.8100  6.2512 

6.8101  6.2510   6.81007   6.2512   27.944 
34.65   0.9364  10.4426 

10.9362  10.4425 

10.9363  10.4425 

10.9363  10.4427  10.9363   10.44257  24.687 

59.75   10.8000  10.3701 

10.8002  10.3703 

10.8002  10.3702 

10.8001  10.3699  10.8001   10.37012  21.499 
10.8000 

TABLE  9. — Ethyl  propionate. 

6.7887  6.2480 

6 . 7888  6 . 2480 
6.7888   6.2478 

6.7887   6.2478   6.78875   6.2479   27.043 

33.89   9-8185  9-3356 

.  9.8187  9.3356 

9.8186  9-3355 

9.8186  9-3356   9.8186    9-33557  24.152 

59.15   10.7920  10.3682 

10.7921  10.3682 

10.7920  10.3681 

10.7919  10.3680  10.7920   10.36812  21.194 

TABLE  10. — Methyl  isobutyrate. 

10.0  9.8776   9-3452 
9-8775   9-3450 
9-8773   9-3451 

9.8776   9-3452   9-8775    9-34512  26.619 

33.87   9-8085  9-3336 

9.8084  9-3337 

9.8083  9-3335 

9.8083  9-3338 

9.8087  9.3338   9-80845   9-33366  23.740 

10. i  9.7385   9-3260 
9-7386   9-3261 

9-3259 
9-3259 
9-3259  9  73862  9  32594  20.634 


13 

TABLE  n. — Methyl  butyrate. 
t.  A.  B.  c.  D.  D.W. 

10. o    8.3627  7-8043 

8.3626  7.8042 

8.3627  7.8042 

8.3625  7.8042   8.36262   7.80422  27.92 

34.8    8.2869  7-7885 

8.2867  7.7885 

8.2868  7.7885 

8.2868  7.7885       8.2868         7-7885       24.915 

59.85       8.2217  7-7824 

8.2218  7.7824 

8.2217  7-7824 

8.2216  7.7824       8.22168       7.7824       21.964 
8.2216 


SURFACE  TENSION. 
TABLE  12.  —  Methyl  formate. 


t.  >R.  &  S.1.  r-  From  curves,     (w  ~  —  ) 


20.  o  24.64  24.11 

30.0  23.09  22.72* 

40.0  21.56  21.34* 

50.0  20.05  T9  95* 

60.0  18.58  18.57* 

70.0  17-15  17.19* 


TABLE  13.— Amyl  formate. 

t.  r  H.  &  G.2  r-  Prom  curve  S.     (w  *-""' 

43.8  21.64  21.51 

77.8  18.40  18.12* 

109-2  I5-52  I5-05* 

1  Ramsay  and  Shields,  Zeit.  phys.  Chem.,  1893. 

2  Homfray  and  Guye,  Jour,  de  Chem.  Phys.,  1903,  i. 


14 
TABLE  14. — Ethyl  acetate. 


2.106 


/. 

r-                                                  r.     From  curve  S.    (  w  ~  1 
v      2.3373^ 

9-5 

24.71       G.  &  B.1        24.05 

12.9 

24.14       R.  &G.2       23.74 

20.  o 

23.60       R.  &S.          22.82 

3i-3 

21.87       R.  &G.         21.43 

46.9 

20.11       R.  &G.         19.63 

55-o 

19.06       R.  &G.         18.70 

55-6 

18.82       G.  &  B.          18.63 

65-9 

17.76       R.  &G.         1745* 

73-5 

17.07       R.  &G.         16.57* 

77.0 

16.63       G.  &  B.         16.17* 

80.0 

16.32       R.  &S.          15-83* 

90.0 

15.14       R.  &S.          14.67* 

IOO.O 

13.98       R.  &S.          13-53* 

TABLE  15.  —  Methyl  isobutyrate. 

j 

,      2.no8x 

*. 

f  R.  &  G.                      y*               Fiom  curve  o.      f  zf              j 

10.5 

24.06        24.03 

30-5 

21.82            21.  81 

41  .0 

20.63           20.68 

55-o 

19.  18            19.  18 

75-o 

17.02            17.  04* 

86.6 

15.78            15.80* 

TABLE  16.  —  Ethyl  formate. 

r  = 

0.01843  cm.                     r  =  0.01046  cm. 

/. 

r  R.  &  A.8                r  R  &  A.             r  from  curve  S. 

IO.O 

24.08                    24.22                    24.18 

46-5 

19.50                    I9.7I                     19.68* 

78-5 

15.68                    15.68                    15-73* 

TABLE  17. — Methyl  acetate. 
r  —  0.01843  cm.  r  =  0.01046  cm. 

/.  rR-&A.  r  R-  &  A.  j- from  curve  S. 

10.0  25.22  25.06  25.23 

46.2  20.32  20.49  20.29* 

78.3  16.28  16.35  15-89* 

1  Guye  and  Baud,  Arch,  des  Sci.  Phys.  et  Nat.,  4  s.,  Vol.  n. 

2  Renard  and  Guye,  Jour,  de  Chem.  Phys.,  1907,  5. 

3  Ramsay  and  Aston,  Zeit.  phys.  Chem.,  15  (1894),  Part  i. 

*A11  values  thus  marked  were  extrapolated  beyond  points  on  curve. 
T  K  =  2.106  being  a  mean  of  R.  &  S.  and  R.  &  G. 


TABLE  18. — Propyl  formate. 


r  =  0.01843  cm. 

r  =  0.01046  cm. 

t.                    r  R-  &  A. 

r  R.  &  A.             r  from  curve  S. 

10.  o               25.02 

25.06                    24.81 

46  .  2                       20  .  67 

20.71                    20.83 

78.2                        17.52 

17.44                    17-61* 

TABLE  19.  —  Methyl  propionate. 

r  =  0.01708  cm. 

r  =  0.01046  cm. 

/.                      r  R.  &  A. 

r  R  &  A.              r  from  curve  S. 

10.  o               25.23 

25-5I                     25.36 

46.2                   20.85 

20.98                     2  I.  08 

78.2                   17.11 

17.26                      17.30* 

TABLE  20.- 

—  Propyl  acetate. 

r  =  0.01708  cm. 

r  =  0.01046  cm. 

t.                          rR.&A. 

r  R.  &  A.            r  from  curve  S. 

10.  o               24.00 

24  .88               24  .  69 

46  .  2                20  .  86 

20.84                    20.71 

78-2                17-35 

17.41                    17.36* 

TABLE  21.  —  Ethyl  propionate. 

r  =  0.01708  cm. 

r  =  0.01046  cm. 

/.                 rR.  &A. 

r  R.  &  A.              r  from  curve  S. 

10.  o               24.57 

24.57                    24.54 

46.2               20.58 

2O.62                    2O.6O 

78.2                17.24 

17.22                    17.20* 

TABLE  22.  —  Methyl  isobutyrate. 

r  =  0.01708  cm. 

r  —  0.01046  cm. 

t.                    r  R.  &  A. 

r  R.  &  A.             r  from  curve  S. 

10.  0                  24.11 

24.08                    24.16 

46.2                  20.29 

20.04                    2O.22 

78.2                   16.70 

16.64                    16.78* 

TABLE  23.- 

-Methyl  butyrate. 

r  =  0.01843  cm.    | 

r  =  0.01046  cm. 

t.                     rR.  &A. 

r  R.  &  A.              r  from  curve  S. 

10.  o               25.63 

25.50                   25.34 

46  .  2                       2  I  .  50 

•      21.39                    21.40 

78.2                        18.15 

18.05                    I7-98* 

*A11  values  thus  marked  were  extrapolated  beyond  points  on  curve. 


i6 

In  Tables  24-29  are  given  the  critical  temperatures  of 
various  investigators  using  the  K  as  indicated  in  the  tables. 
It  is  rather  difficult  to  compare  directly  these  results  with  those 
obtained  by  the  drop  weight  method. 

In  Tables  25-27  with  ethyl  acetate  it  may  be  seen  that  the 
results  agree  well  although  differences  in  temperature  are 
considerable. 

Comparing  Table  24  with  Table  38  (methyl  formate)  it  will 
be  noticed  that  the  critical  temperatures  do  not  agree  as  well 
as  might  be  expected,  but  this  may  be  well  explained  by 
polymerization  at  the  higher  temperatures. 

In  Tables  25-27  and  43  (ethyl  acetate)  the  results  in  43 
show  a  closer  agreement  with  those  of  Young  than  with  those 
of  other  workers. 

In  Tables  29  and  41  (amyl  formate)  the  results  in  41  also 
show  a  closer  agreement  with  those  determined  experimentally. 

In  Tables  30-37  the  differences  between  the  critical  tem- 
peratures determined  with  different  tubes  are  quite  noticeable, 
while  with  Tables  39,  40,  42-48  will  show  very  good  agree- 
ment. 

From  these  agreements  of  critical  temperatures  calculated 
in  Tables  38-48  it  may  be  stated  that  a  liquid  which  will  give 
the  same  critical  temperature  at  various  expeiimental  tem- 
peratures has  normal  molecular  weight.  Those  liquids  which 
do  not,  are  either  associated  or  as  in  this  case  decomposed 
at  the  higher  temperatures.  After  working  for  some  time 
with  the  formates,  it  became  quite  evident  that  an  explanation 
was  necessary,  in  view  of  the  non- concordant  results  that  were 
obtained,  there  being  a  general  trend  in  the  calculated  critical 
temperatures  with  variation  of  temperature.  It  was  decided 
to  investigate  the  effect  of  heat  on  several  of  the  formates, 
those  chosen  being  propyl  and  amyl  formate. 

Propyl  formate  was  heated  for  two  and  one-half  hours  at 
60°  under  atmospheric  pressure  and  allowed  to  cool  slowly 
to  room  temperature. 

Unheated  sample  gave  drop  weight  at  10.0°  =  27.337. 

Heated  sample  gave  drop  weight  at  10.0°  =  27.434  deter- 
mined immediately. 


17 

Heated  sample  gave  drop  weight  at  10.0°  =  27.430  after 
1 6  hours. 

Heated  sample  gave  drop  weight  at  10.0°  =  27.366  after 
10  days. 

Another  sample  was  heated  similarly  and  cooled  suddenly 
to  0.0°  and  the  drop  weight  immediately  determined  which 
gave  27.337. 

These  results  show  that  some  change  had  taken  place  which 
was  apparently  reversible  and  which  is  influenced  largely  by 
time  and  temperature. 

Amyl  formate  was  heated  to  230°  in  a  sealed  tube  with  a 
small  amount  of  mercury  for  three  and  three-fourths  hours. 
On  opening  the  thoroughly  cooled  tube  considerable  pressure 
was  noticed. 

Unheated  sample  gave  drop  weight  at  10.0°  =  27.464. 

Heated  sample  gave  drop  weight  at  10.0°  =  27.309. 

In  both  cases  a  decided  differences  of  odor  was  noticed  be- 
tween the  heated  and  unheated  samples.  As  an  explanation 
for  this  variation  it  may  be  assumed  to  be  due  to  polymerization 
for  lack  of  more  confirmatory  evidence.  Polymerization  at 
higher  temperatures  has  been  noticed  by  Young  and  Thomas1 
in  the  case  of  the  formates  and  by  Homfray  and  Guye2  with 
liquids  such  as  ethyl  lactate.  However  Smiles3  states  "it  is 
doubtful  that  the  effect  of  temperature  is  related  to  the  chemical 
constitution  of  the  liquid."  The  formates,  then  may  be 
classed  as  the  exceptions  to  the  statement  of  Gossart4  "that 
the  temperature  coefficient  is  the  same  for  substances  of  the 
same  class,"  although  his  measurements  deal  only  with  the 
alcohols,  acids,  esters  and  some  chlorine  derivatives. 

CRITICAL  TEMPERATURE. 

The  following  were  calculated  from  the  results  of  Ramsay 
and  Shields5  using  K  =  2.1012. 

1  Young  and  Thomas,  Trans.  Chem.  Soc.,  1893. 

2  Homfray  and  Guye,  Jour,  de  Client.  Phys.,  1903,  i. 

3  Smiles,  Text-book,  relations  between  chem.  constitution  and  some 
physical  properties,  1910. 

4  Gossart,  Ann.  chim.  phys.,  [6]  19173  (1890). 

5  Ramsay  and  Shields,  Zeit.  phys.  Chem.,  1893. 


i8 
TABLE  24. — Methyl  formate. 

r(P%  T, 

20.0  383.9  208.70 

30.0  363-7  209.09 

40.0  343.2  209.33 

50.0  322.6  209.53 

60 . o        302 . 5         209 . 96 

70.0        282.7         210.54 

190.0         37.7         213.94 

200.0  19.2  215.13 

211. 0  4-0  217.89 

TABLE  25. — Ethyl  acetate. 

20.0  500.7  264.29 

80.0  367 .2  260.75 

90.0  344.4  259.90 

100. o  321.7  259.10 

no.o  299.0  258.29 

120.0  277.1  257.87 

245.0  7-2  254.42 

The  following  were  calculated  from  the  results  of  Guye  and 
Baud1  using  K  =  2.1012. 

TABLE  26.— Ethyl  acetate. 

K*)2"- 

9-5  5I9-6  262.78 
55-6  413-0  258.15 
77-o  373-o  260.51 

The  following  were  calculated  from  the  results  of  Renard 
and  Guye2  using  K  =  2.1108. 

TABLE  27. — Ethyl  acetate. 

K")*- 

12.0  509.0  260.04 

31.3  470.0  259.96 

46-9  437-0  259.93 

55-o  418.0  259.02 

65-9  394-0  258.55 

73-5  381-0  259.99 

1  Guye  and  Baud,  Arch.  Sci.  Phys.  et  Nat.,  4  s.,  Vol.  n. 

2  Renard  and  Guye,  Jour,  Chimie  Physique,  5,   1907. 


TABLE  28. — Methyl  isobutyrate. 


io-5  563-o  283.22 

30.5  519.0  282.37 
41.0  496.0  281.98 
55.0  467.0  282.24 
75.0  422.0  280.95 

86.6  396.0  280.25 

The  following  were  calculated  from  the  results  of  Homfray 
and  Guye1  using  K  =  2.1012. 

TABLE  29. — Amyl  formate. 
/.  r(^)2/3'  ^c- 

43-8  569-5  320.83 

77-8  497-8  320.71 

109.2  432.2  320.89 

The  following  were  calculated  from  the  results  of  Ramsay 
and  Aston2  using  K  =  2.1212. 

TABLE  30. — Ethyl  formate. 
r  =  0.01843  cm.  r  =  0.01046  cm. 

10. o  443-5  225.07  446.0  226.25 

46-5  371-5  227.63  375.5  227.51 

78.5  309-2  230.17  309.1  230.22 

TABLE  31. — Methyl  acetate. 

r  =  0.01843  cm.  r  =  0.01046  cm. 

10. o             462.8           234.17  459-9           232.90 

46.2  383-9     233.17  387.2     234.53 

78.3  3i8.2     234.30  319.5     234.91 

TABLE  32. — Propyl  formate. 
r  =  0.01843  cm.  r  =  0.01046  cm. 

10. o  523.6  262.83  524-4  263.21 

46.2  446-3  262.59  447.1  262.97 

78.3  387-0  266.64  385.2  265.79 

1  Homfray  and  Guye,  Jour,  de  Chem.  Phys.,  1903,  i. 

2  Ramsay  and  Aston,  Jour.  Chem.  Soc.  Trans.,  65,  1894. 


20 


TABLE  33. — Methyl  propionate. 
r  =  0.01708  cm.  r  =  0.01046  cm. 


IO.O 

46.2 

78.2 

524.3        263.16 
447.3        263.07 
378.8       262.77 

530.2           265.95 
450.2           264.39 
381.9           264.28 

TABLE  34.  —  Propyl 

acetate. 

r  =  0.01708  cm. 

r  =  0.01046  cm. 

I. 

r(^)2/3-                  TV 

r(^?)  '3               ^c' 

IO.O 

46.2 

78.2 

580.2              289.52 
503.0             289.32 
431.0             287.38 

582.0           290.34 
502.2           288.94 
432.3           287.99 

TABLE  35.  —  Ethyl  propionate. 

r  =  0.01708  cm. 

r  =  0.01046  cm. 

IO.O 

46.2 

78.2 

574.0           286.59 
496.1           286.07 
428.1           286.01 

576.2           287.63 
496.9           286.44 

427.8           285.87 

TABLE  36.  —  Methyl  isobutyrate. 

r  =  0.01708  cm. 

r  =  0.01046  cm. 

IO.O 

46.2 

78.2 

563.6           281.69 
487.3           281.92 
415.0           279.84 

563.0           281.41 
486.1            281.30 
415.1            279.88 

TABLE  37.  —  Methyl  butyrate. 

r  =  0.01843  cm. 

r  =  0.01046  cm. 

IO.O 

46.2 

78.2 

595.0           296.50 
514.5           294.74 
446.9           294.88 

591.7           294.94 
511.8           293.47 
444-4           293.70 

TABLE  38.  —  Methyl 

formate. 

59.86.     Tc  =  214°   Young 

/2.  IOI2X 

1             v     nf,  I                                 1 

—  • 

.    ••            —   w  \  ' 
V2-3373/ 

t. 

D.  W.                       d.                   W(^ 

)%•             TC.                      r. 

0.  I 

6-7 

IO.O 

16.4 

27.82 

29.893           1.00300          456. 

28.86         0.99354       443- 
28.243       0.98892       435. 
27.36         0.97943       424. 
25.614       0.96320       401. 

50         201.41          26.873 

53       202.46       25.945 
39       202.27       25.390 
51        204.02        24.596 
86       205.75        23.027 

S.  Young,  Sci.  Proc.  Roy.  Dub.  Soc.,  12,  p.  374. 


21 

TABLE  39.— Ethyl  formate. 


M     —     T-2    £ 

\-\       T 

/^  ••>  f    <*i 

o  Vi~k»ii 

/2 

.1212 

\ 

-    l  J.c 

'o*           < 

:          ^OO-J       A  *-"•"  X5-    "•}"'       «M' 

•3373^ 

t.                D.  W. 

d. 

,M^2/3                       T<.                                ^ 

0, 

i 

27 

•993 

0.94697 

510 

.86 

224 

.66 

25 

401 

6 

o 

27 

•17 

0 

•93958 

499 

•59 

225 

•25 

24 

658 

10. 

0 

26.638 

0 

•93458 

490 

•42 

225 

.82 

24 

175 

17 

0 

25.68 

0.926l8 

475 

.64 

226 

•50 

23. 

306 

33- 

95 

23 

.388 

O 

.90418 

440 

.18 

228 

.27 

21 

226 

TABLE 

40.  —  Propyl 

formate. 

M 

87.8 

.     Tc 

== 

264.85 

0  Young. 

r  -  * 

(2 

.  1212 

\ 

— 

2 

•3373/ 

o. 

I 

28 

.604 

o 

.92850 

593 

.69 

260 

.  10 

2f; 

960 

5- 

4 

27 

.941 

o 

92251 

582 

•44 

260 

59 

25- 

358 

10. 

0 

27 

•337 

0.91726 

572 

.01 

260 

.72 

24. 

809 

17 

o 

26 

•458 

0 

90909 

556 

•93 

261 

.27 

24 

OI2 

34- 

75 

24 

.298 

0.88873     519 

•25 

262 

.90 

22, 

051 

60. 

3 

21 

.419 

o 

•85837 

468 

.46 

266 

.72 

19 

439 

TABLE  41.— 

Amyl 

formate. 

M 

116. 

i    IV 

104-6° 

Palewski.1 

Hf*  * 

.  IOI2 

\ 

V 

J\  ~ 

\2 

•3373 

/ 

10. 

0 

27 

.464 

0 

,8882 

706 

.26 

318 

.60 

24- 

686 

35- 

0 

24 

.69 

0. 

8682 

645 

•73 

317 

30 

22  . 

199 

60. 

I 

21 

.904 

o. 

8420 

584 

.62 

316 

,20 

19- 

691 

TABLE 

42.  —  Methyl 

acetate. 

M 

=  73.83.     Tc  = 

233.7 

0  Young. 

(2  . 

I2I21 

) 

r 

2. 

3373> 

0. 

i 

29 

.301 

0. 

95900 

530 

.26 

232. 

96 

26. 

592 

10. 

0 

27 

.801 

0. 

94652 

507 

•53 

233- 

13 

25- 

231 

34 

20 

24 

.16 

o. 

91491 

.16 

233. 

22 

21  . 

926 

TABLE  43.—  Ethyl 

acetate.* 

M 

= 

87.8 

Tc  =  250.1°  Young,      7  —  w(— 

I2I2\ 

3373/ 

0. 

I 

27 

•94 

0. 

92421 

581 

•  71 

254- 

97 

25- 

175 

34- 

6 

23 

•375 

0. 

88277 

501 

.68 

255- 

23 

21  . 

062 

60. 

5 

20 

.064 

0. 

85019 

441 

•63 

255- 

44 

18. 

078 

1  Palewski,  Ber.  Chem.  Ges.,  15,  1882,  p.  2463.  His  results  are  prob- 
ably for  the  same  ester  as  was  used  in  this  investigation. 

*K  used  for  calculation  of  7  was  2.106,  being  the  mean  of  that  of 
R.  &  S.  and  R.  &  G. 


22 

TABLE  44. — Propyl  acetate. 

(2    1 2  1 2 \ 
J 
'  O\3  /  O/ 


D.W.  d. 


o.i   28.433   0.91000   659.98   288.47   25.804 

34.6   24.148  0.87229  576.55  287.32  21.914 
60.  I   21.208   0.84345   517-83   287.74   19.246 


TABLE  45. — Methyl  propionate. 
M  =  87.8.     Tc  =  257.4°  Young.       r  - 

10. o  27.944  0.92678  580.70  264.44  25.360 
34.65  24.687  0.89758  524.08  264.87  22.405 
59.75  21.499  0.86682  467.11  264.59  19-511 


TABLE  46. — Ethyl  propionate. 
M  =  101.77-     Tc  =  272.9°  Young.     r  =  ^(2.3373) 

10.0  27.043  0.90106  631.86  286.32  24.543 
33.89  24.152  0.87435  575-74  286.21  21.919 
59.15  21.194  0.84502  516.87  286.28  19.234 


TABLE  47. — Methyl  isobutyrate. 
M  =  101.77-    Tc=  267. 55°  Young.    r  =  ^(2.3373) 

00. o  26.619      0.90033       622.30       282.24       24.158 
33.87     23.740      0.87328       566.39       282.19       21.545 

10. i  20.634       0.84295       504.03       281.74       18.726 


TABLE  48. — Methyl  butyrate. 
M  =  101.77-     Tc  =  281.3°  Young,  2 3373 

10.  o  27.92  0.90925  648.44  293.42  25.338 
34.8  24.915  0.88175  590.62  293.68  22.610 
59.85  21.964  0.85375  53x-99  293.45  I9-932 


SUMMARY. 
As  a  result  of  this  investigation  we  have  shown : 

1.  That  the  drop  weight  method,  in  connection  with  the 
new  definition  of  normal  molecular  weight  of  Morgan,  is  the 
most  accurate  method  known  for  the  determination  of  molec- 
ular weight  in  the  liquid  state. 

2.  That  the  surface  tension  of  a  liquid  may  be  most  easily 
and  exactly  calculated  by  this  method,  and  that  a  knowledge 
of  density  of  the  liquid  is  unnecessary,  a  factor  which  may  be 
responsible  for  some  of  the  poor  results  which  are  found  in  the 
literature. 

3.  That  the  definition  of  normal  molecular  weight  in  the 
liquid  state,  i.  e.,  such  a  liquid  that  it  will  give  the  same  value 
of  Tc  at  all  temperatures  of  observation,  shows  that  all  the 
above  liquids  with  the  exception  of  the  formates,  are  non- 
associated,  i.  e.,  normal  in  molecular  weight,  and  that  the 
formates  undergo  a  reversible  reaction  at  higher  temperatures, 
which  makes  them  appear  abnormal. 


BIOGRAPHY. 

Frederick  William  Schwartz  was  born  in  Albany,  N.  Y., 
September  2,  1883.  He  entered  the  Rensselaer  Polytechnic 
Institute  at  Troy,  N.  Y.,  in  1901,  and  graduated  in  1905  with 
the  degree  of  B.S.  He  attended  Columbia  University  during 
the  summers  of  1908,  1909,  1910  and  also  from  September, 
1910.  Since  graduation  from  Rensselaer  he  has  been  assistant 
in  chemistry  at  Rensselaer. 


•  ••. 

' 


UNIVEESITY   OF   CALIFOENIA   LIBBAEY, 
BEEKELEY 


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